Convergence towards attractors for a degenerate Ginzburg-Landau equation |
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Authors: | N I Karachalios N B Zographopoulos |
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Institution: | (1) Department of Mathematics, University of the Aegean, Karlovassi, 83200 Samos, Greece;(2) Department of Applied Mathematics, University of Crete, 71409 Heraklion, Greece |
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Abstract: | We study a real Ginzburg-Landau equation, in a bounded domain of
with a variable, generally non-smooth diffusion coefficient having a finite number of zeroes. By using the compactness of the embeddings of the weighted Sobolev spaces involved in the functional formulation of the problem, and the associated energy equation, we show the existence of a global attractor. The extension of the main result in the case of an unbounded domain is also discussed, where in addition, the diffusion coefficient has to be unbounded. Some remarks for the case of a complex Ginzburg-Landau equation are given.Received: May 6, 2002; revised: October 3, 2002 |
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Keywords: | 35B40 35B41 35R05 |
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